Question: What is the value of the following logarithm? $\log_{11} \left(\dfrac{1}{121}\right)$
Solution: If $b^y = x$ , then $\log_{b} x = y$ Therefore, we want to find the value $y$ such that $11^{y} = \dfrac{1}{121}$ In this case, $11^{-2} = \dfrac{1}{121}$, so $\log_{11} \left(\dfrac{1}{121}\right) = -2$.